(2a+b)(a+b)=

Solution for (2a+b)(a+b)= equation:

Simplifying
(2a + b)(a + b) = 0

Multiply (2a + b) * (a + b)
(2a * (a + b) + b(a + b)) = 0
((a * 2a + b * 2a) + b(a + b)) = 0

Reorder the terms:
((2ab + 2a2) + b(a + b)) = 0
((2ab + 2a2) + b(a + b)) = 0
(2ab + 2a2 + (a * b + b * b)) = 0
(2ab + 2a2 + (ab + b2)) = 0

Reorder the terms:
(2ab + ab + 2a2 + b2) = 0

Combine like terms: 2ab + ab = 3ab
(3ab + 2a2 + b2) = 0

Solving
3ab + 2a2 + b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + b)(a + b) = 0

Subproblem 1
Set the factor '(2a + b)' equal to zero and attempt to solve:

Simplifying
2a + b = 0

Solving
2a + b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Subproblem 2
Set the factor '(a + b)' equal to zero and attempt to solve:

Simplifying
a + b = 0

Solving
a + b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

Simplifying
a = -1b
Solution
a = {-0.5b, -1b}